In humans, Mitogen-Activated Protein Kinases (MAPKs) protect cells against ischemia, hyper-osmolarity, uv-irradiation and other stressors. Dysregulated MAPK pathways contribute to diseases such as Alzheimer's Disease, Amyotrophic Lateral Sclerosis and cancer. In this proposal we detail a multi-disciplinary research plan that combines mathematical modeling, biochemical and genetic experimentation, and live-cell imaging to better understand how MAPKs coordinate cellular responses to environmental stress. Using an innovative biochemical technique, we have recently accumulated experimental evidence that strongly suggests that rapid signal activation in the yeast High-Osmolarity Glycerol (HOG) Pathway is encoded via positive feedback, and that pathway deactivation occurs via delayed negative feedback. The HOG pathway transmits the presence of hyper-osmotic stress to the nucleus of a cell through the MAPK Hog1, a homolog to the mammalian MAPKs p38 and JNK. Two distinct signaling branches (Sho1 and Sln1) activate Hog1. In Aim 1a) we use mathematical modeling to identify the most likely HOG pathway feedback network that dynamically regulates the MAPK in response to sustained hyper-osmotic stress. We demonstrate that our modeling approach has thus far been successful by presenting a model that agrees with our preliminary experimental data. In Aim 1b) we then extend our mathematical models to predict how the MAPK will respond to transient hyper-osmotic stress. We test the model predictions by experimentally exposing yeast to transient applications of salt induced hyper-osmotic stress and measure MAPK phosphorylation levels and nuclear translocation of a MAPK-GFP construct through live-cell imaging. In Aim 2a) we construct a yeast strain that is absent feedback regulation by deleting the Sho1 trans-membrane osmo-sensor that activates the Sho1 branch. We use this construct (sho1?) to measure MAPK phosphorylation in the Sln1 branch. We then use our preliminary data, mathematical models and parametric sensitivity analysis to understand how each branch (Sho1 and Sln1) contributes to MAPK phosphorylation. Finally, we measure the MAPK-GFP nuclear translocation rate in each strain to determine how each branch individually contributes to MAPK activation. Ultimately, the combination of these aims will allow us to better understand how feedback regulation and branched pathways contribute to MAPK activity. This work is significant because it will establish signaling mechanisms that allow multiple pathways to contribute to stress adaptation. Because many signaling mechanisms initially discovered in yeast have proven to be conserved across many cell types, including human, we expect our results to impact our understanding of human disease.